Deriving the Hamiltonian of a system

AI Thread Summary
To derive the Hamiltonian for the given system with the Lagrangian L=ř^2/(2w) - wr^2/2, the relationship H=př-L is used, where ř represents the first derivative of position r. The user attempts to solve the problem but has not yet learned how to properly write equations, instead providing images of their work. Feedback indicates that the user needs to focus on deriving the Hamiltonian equation rather than the Hamiltonian itself, starting from the Lagrangian equation of motion. The discussion emphasizes the importance of correctly applying the principles of Hamiltonian mechanics. Understanding these concepts is crucial for accurately deriving the Hamiltonian.
middleearthss
Messages
13
Reaction score
1

Homework Statement


Derive the Hamiltonian equation in terms of momentum and position ( p and r) for the given system whose lagrangian is stated as L=ř^2/(2w) - wr^2/2

Homework Equations


L=ř^2/(2w) - wr^2/2 and H=př-L

The Attempt at a Solution


Notice here ř means first derivative of r. As i haven't learned how to write equations i derives a solution whoch looks correct and took a picture. I am hoping you can see if it is correct and point at mistakes. In the work i exchanged r with q.
Here are the links to 2 photos i took[/B]
http://www.photobox.co.uk/my/photo?album_id=3508111407&photo_id=8712540967#8712540967

http://www.photobox.co.uk/my/photo?album_id=3508111407&photo_id=8712541232#8712541232

 

Attachments

  • 20150624_191910.jpg
    20150624_191910.jpg
    37 KB · Views: 414
  • 20150624_191918.jpg
    20150624_191918.jpg
    38.6 KB · Views: 380
Physics news on Phys.org
It says You cannot access this album
 
You need hamiltonian equation, not the Hamiltonian. So start from lagrangian equation of motion.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Deriving ODEs for straight lines in polar coordinates for a given Lagrangian
Replies
8
Views
1K
Equivalence of Euler-Lagrange equations and Cardinal Equations for a rigid planar system
Replies
4
Views
1K
How to parametrize motion of a pendulum in terms of Cartesian coordinates?
Replies
1
Views
1K
How Do You Calculate Static Forces in a Trebuchet's Throwing Arm?
Replies
9
Views
3K
Deriving the Hamiltonian of a system given the Lagrangian
Replies
2
Views
1K
To find the forces acting in a system in equilibrium
Replies
5
Views
1K
I Hamiltonian of the bead rotating on a horizontal stick
Replies
3
Views
2K
Solid Disk Pulley + 2 Mass system, v derivation using 2 methods
Replies
12
Views
2K
How to Apply Derivatives in Physics Problems?
Replies
9
Views
1K
How to find voltage across capacitor in RLC circuit?
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top